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Table 2 Results of the proposed greedy algorithm (SEQ) versus the MIS-based algorithm and upper (UB) and lower bound (LB) as determined by Gurobi 5.6 solver within 3,000 s

From: Efficiently identifying critical nodes in large complex networks

Graph k LB UB SEQ MIS Graph k LB UB SEQ MIS
ER125 5 405 405 851 715 ER150 5 4,277 4,277 4,972 5,471
ER125 10 133 133 151 199 ER150 10 837 2,301 2,678 4,862
ER125 15 66 66 76 81 ER150 15 347 347 976 890
ER125 20 36 36 44 43 ER150 20 167 167 220 410
ER125 25 20 20 23 24 ER150 25 94 94 101 201
ER125 30 9 9 12 15 ER150 30 58 58 69 124
ER125 35 3 3 7 10 ER150 35 36 36 44 79
ER125 40 0 0 2 5 ER150 40 22 22 29 52
ER125 45 0 0 0 0 ER150 45 14 14 16 36
ER125 50 0 0 0 0 ER150 50 8 8 11 22
BA200 5 818 818 818 1,073 BA250 5 782 782 782 1,235
BA200 10 297 297 298 668 BA250 10 342 342 342 626
BA200 15 156 156 156 413 BA250 15 221 221 221 462
BA200 20 104 104 104 304 BA250 20 143 143 143 355
BA200 25 70 70 70 206 BA250 25 105 105 105 293
BA200 30 48 48 48 164 BA250 30 77 77 77 243
BA200 35 33 33 33 135 BA250 35 60 60 60 213
BA200 40 20 20 22 114 BA250 40 45 45 45 183
BA200 45 15 15 17 98 BA250 45 30 30 30 158
BA200 50 10 10 12 77 BA250 50 21 21 23 135
WS100 5 2,766 4,465 4,465 4,465 WS125 5 4,578 7,140 7,140 7,140
WS100 10 1,054 2,941 4,005 4,005 WS125 10 1,796 6,005 6,555 6,555
WS100 15 572 945 3,570 1,784 WS125 15 892 3,642 5,995 5,995
WS100 20 379 495 3,160 1,107 WS125 20 618 3,187 5,460 5,460
WS100 25 234 300 2,775 578 WS125 25 433 708 4,950 1,719
WS100 30 176 219 2,415 414 WS125 30 309 467 4,465 758
WS100 35 132 148 2,080 271 WS125 35 239 344 4,005 480
WS100 40 98 103 1,770 159 WS125 40 195 246 3,570 370
WS100 45 70 72 1,485 94 WS125 45 152 180 3,160 278
WS100 50 48 48 1,225 67 WS125 50 117 137 2,775 207
FF125 5 3,237 3,643 3,874 5,280 FF150 5 5,895 7,789 7,660 7,789
FF125 10 872 1,805 2,202 2,588 FF150 10 2,362 9,591 6,252 6,711
FF125 15 318 318 1,198 515 FF150 15 1,491 7,893 5,087 5,819
FF125 20 165 165 773 249 FF150 20 911 3,909 4,043 5,192
FF125 25 111 111 422 158 FF150 25 561 1,967 3,359 4,319
FF125 30 73 73 118 103 FF150 30 339 1,237 2,322 3,869
FF125 35 46 46 65 69 FF150 35 216 380 1,874 693
FF125 40 29 29 40 45 FF150 40 159 174 1,275 344
FF125 45 16 16 25 31 FF150 45 105 117 793 240
FF125 50 11 11 15 21 FF150 50 79 79 321 155
  1. The networks are those presented in [20].